If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?
A. 2
B. 3
C. 4
D. 6
E. 9
OA B
Source: Veritas Prep
If x is the greatest common factor of 36 and 96, what is the
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36 = 2*2*3*3BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?
A. 2
B. 3
C. 4
D. 6
E. 9
96 = 2*2*2*2*2*3
GCF = the product of the factors in blue = 2*2*3 = 12.
Sum of the digits = 1+2 = 3.
The correct answer is B.
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Mitch's solution is the approach I'd take, but another way to answer this question is to simply LIST the factors of each value and then find the GREATEST factor they have in common.BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?
A. 2
B. 3
C. 4
D. 6
E. 9
OA B
Source: Veritas Prep
When listing factors, it's best to do so in pairs of values with a given product (either 36 or 96). Here's what I mean:
Factors of 36 = {1, 36}
= {1, 2, 18, 36}
= {1, 2, 3, 12, 18, 36}
= {1, 2, 3, 4, 9, 12, 18, 36}
= {1, 2, 3, 4, 6, 9, 12, 18, 36}
Following the same approach, we see that the factors of 96 are {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}
When we examine both sets of factors, we see that the greatest common factor is 12 (i.e., x = 12)
What is the sum of the digits of x?
1 + 2 = 3
Answer: B
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36 = 2^2 x 3^2BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?
A. 2
B. 3
C. 4
D. 6
E. 9
96 = 48 x 2 = 8 x 6 x 2 = 2^5 x 3^1
The GCF is the product of the prime factors that both numbers have in common. So the GCF of 36 and 96 is 2^2 x 3^1 = 12 and the sum of the digits of 12 is 1 + 2 = 3.
Answer: B
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